TY - JOUR
T1 - Solvability of Hessian quotient equations in exterior domains
AU - Dai, Limei
AU - Bao, Jiguang
AU - Wang, Bo
N1 - Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society.
PY - 2025/2/1
Y1 - 2025/2/1
N2 - In this paper, we study the Dirichlet problem of Hessian quotient equations of the form Sk (D2u)/Sl (D2u) = g(x) in exterior domains. For g ≡ const., we obtain the necessary and sufficient conditions on the existence of radially symmetric solutions. For g being a perturbation of a generalized symmetric function at infinity, we obtain the existence of viscosity solutions by Perron's method. The key technique we develop is the construction of sub- and supersolutions to deal with the non-constant right-hand side g.
AB - In this paper, we study the Dirichlet problem of Hessian quotient equations of the form Sk (D2u)/Sl (D2u) = g(x) in exterior domains. For g ≡ const., we obtain the necessary and sufficient conditions on the existence of radially symmetric solutions. For g being a perturbation of a generalized symmetric function at infinity, we obtain the existence of viscosity solutions by Perron's method. The key technique we develop is the construction of sub- and supersolutions to deal with the non-constant right-hand side g.
KW - asymptotic behavior
KW - exterior Dirichlet problem
KW - Hessian quotient equations
KW - necessary and sufficient conditions
KW - radially symmetric solutions
UR - https://www.scopus.com/pages/publications/86000377140
U2 - 10.4153/S0008414X23000834
DO - 10.4153/S0008414X23000834
M3 - Article
AN - SCOPUS:86000377140
SN - 0008-414X
VL - 77
SP - 118
EP - 148
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
IS - 1
ER -